I actually tried to login with my wife's Apple ID into iTunes on my Mac. iTunes tried to upload music to my wife's iCloud Library, but most of the albums showed up in the iCloud as greyed out and were not accessible. Only a small minority of songs uploaded that way could be accessed from iCloud. So that did not really work.
Quite a few of the albums in my iTunes library were purchased before Apple Music. My family members cannot access them despite the fact that we now have a family plan. So it looks like Family Sharing does not apply to music purchased before you setup Family Sharing.
It seems now that the only way to proceed is to create duplicate iTunes accounts and libraries with music that's not available through Apple Music catalogue. If you ask me, it's a total waste of resources, as I now have to duplicate gigabytes of music on my Mac.
I wish Apple would let us to use both iCloud and iTunes libraries.
If they are songs you bought you would go to the iTunes app on each of their devices and look in the purchased section under Music. You would then be able to download the songs to your device. If they are songs you gathered from other sources and added to your library you will not be able to use Family Sharing to share the songs. You would (I think) have to upload those songs to their libraries while logged in as them but this is a guess. I'm thinking they would have to get the songs to their collection in the same way you have. The restriction for anything Family Sharing is that it has to be bought through the store then shared to the family.